macroeconomics

Problem Set 3
This is due Nov 2nd. I already attached the excel file for this problem set in blackboard therefore you don’t need a partner in order to do the excel part anymore. However, you may still work with your partner but you have to submit the problem set individually. Do not submit your excel files. I only need the graph and tables that I asked you to do. No email submissions, please.
Part I. Robinson Crusoe
1. Consider Robinson Crusoe in a very big island living all by himself. At t=0, he found the island to have corn trees (corn is actually a grass) equal to K0 = 100 units. In the next period, he harvests the corn according to the production function Y=K.5L.5 (here A=1) and decides how much to eat and how much to plant so that Y = C+I. He then plants the new seeds to add to his old stock of corn trees. Strong wind in the island knocks down 2% of the corn trees in every period so that capital evolves such that Kt+1 = Kt + It – Dept .
a. If Crusoe decides to eat 70% of his harvest in every period, graphically show his production, consumption, and stock of corn trees grow over time.
b. What is the steady state capital and output.
c. What happens to the steady state output and capital if there are insects that eat the trees so that winds and insects knock down 5% of corn trees every period.
d. Redo (a) and (b) if K0 = 300 units.
2. Now suppose he lives only for 2000 periods consumes everything in his last period. Tabulate Crusoe’s total consumption at saving rates = 0.10, 0.30, … 0.90. Where is he most well off, ie, at what saving rate is his consumption rate highest?
3. Now tabulate his total consumption at saving rates = 0.10, 0.30, … 0.90 if he lives for only 100 periods? Where is he most well off?
Part II
4. For a closed economy, GDP is $11 trillion, consumption is $7 trillion, taxes are $2 trillion and the government runs a deficit of $1 trillion. What are private saving and national saving?
5. You have some estimates of national accounts numbers for a closed economy for the coming year. Under one set of expectations, government purchases will be $30 billion, transfer payments will be $10 billion, and taxes will be $45 billion. Under another set of expectations, GDP will be $200 billion, taxes will be $50 billion, transfer payments will be $20 billion, consumption will be $120 million, and investment will be $40 billion. Calculate surplus in the first and second case.
6. Assuming the market for loanable funds is in equilibrium, use the following numbers to determine the quantity of loanable funds supplied.
GDP
$8.7 trillion
Consumption Spending
$3.5 trillion
Taxes Net of Transfers
$2.7 trillion
Government Purchases
$3.0 trillion
7. Suppose the market for loanable funds is in equilibrium. Given the numbers below, determine the quantity of loanable funds demanded.
GDP
$100 billion
Consumption
$65 billion
Taxes Net of Transfers
$15 billion
Government Spending
$20 billion
8. Suppose some country had a population of about 25 million, a labor-force participation rate of 60 percent, and an unemployment rate of 6 percent. How many people were unemployed? How many are employed? How many are not in the labor force?
Numbers 9-11. The monetary policy of Salidiva is determined by the Salidivian Central Bank. The local currency is the salido. Salidivian banks collectively hold 100 million salidos of required reserves, 25 million salidos of excess reserves, 250 million salidos of Salidivian Treasury Bonds, and their customers hold 1,000 million salidos of deposits. Salidivians prefer to use only demand deposits and so the money supply consists of demand deposits.
9. Assuming the only other item Salidivian banks have on their balance sheets is loans, what is the value of existing loans made by Salidivian banks?
10. Suppose the Central Bank of Salidiva loaned the banks of Salidiva 5 million salidos. Suppose also that both the reserve requirement and the percentage of deposits held as excess reserves stay the same. By how much would the money supply of Salidiva change?
11. Suppose the Central Bank of Salidiva purchases 25 million salidos of Salidivian Treasury Bonds from banks. Suppose also that both the reserve requirement and the percentage of deposits held as excess reserves stay the same. By how much would the money supply of Salidiva change?